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\begin{abstract}
In this assignment we use Matlab to explore techniques of collaborative filtering 
that learns from previous movie ratings of the MovieLens 100k Dataset to predict the 
missing user ratings. We provide an algorithm to construct a combined
multiplicative model 
that uses residual fitting. We use Stochastic Gradient Descent with regularization and
to obtain a matrix factorization of rank $k$. We demonstrate how to tune the learning rate
and regularization of our model by minimizing mean squared error and construct a final
model with \optmse{} and \optmae{} for a rank \optk{}. We also discuss the scalability of our
algorithm to the full Netflix dataset. 

\end{abstract}

